Linear and nonlinear optical susceptibilities of orthorhombic rare earth molybdates RE2(MoO4)3

The dielectric responses (i.e. the refractive indices and the second order nonlinear susceptibilities) of all orthorhombic rare earth molybdates have been studied on the basis of the relationship between dielectric responses and the average atomic number of constituent atoms of crystals. Both the linear and second order nonlinear optical responses at 1.064 μm decrease with increasing atomic number from La to Lu.     

Duality Principles in Frame Theory

Duality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article we present a general approach to derive duality principles in abstract frame theory. For each sequence in a separable Hilbert space we define a corresponding sequence dependent only on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract frame setting. In the last part we apply our results to Gabor systems.     

The luminescence of α- and β-LaNb3O9

The luminescence of undoped and rare-earth-doped LaNb₃O₉ is reported. The two modifications (α and β) show striking differences. Whereas undoped β-LaNb₃O₉ does not luminesce at all (down to 4.2 K), α-LaNb₃O₉ emits efficiently with a quenching temperature of 250 K. Energy transfer from niobate to rare-earth dopants is observed for the α, but not for the β modification. The rare-earth dopant emission consists of sharp lines for the α modification, but is considerably broadened for the β modification. The luminescence properties are discussed in terms of the crystal structure. In addition results for α-NbPO₅ will be given.     

2-（1,3-Diphenylpropen-1,3-diolato）-1,3,2-（5-formylbenzo）dioxaborol： A ＇Whole-molecule Disorder＇ Crystal Structure

The boron atom in C22H15BO5 is O,O’-chelated by the anions in a tetrahedral geometry, with the planar five-and six-membered chelate rings being orthogonal to each other. The molecule lies on a two-fold rotation axis. The molecule is disordered with respect to another molecule in a 93:7 ratio; the treatment of the ‘whole-molecule disorder’ by employing a large number of restraints is described. Crystal data: C22H15BO5, monoclinic C2/c, a = 17.1804(5), b = 12.9409(4), c = 9.8842(3) , β = 124.832(2)o, V = 1803.82(9) 3 at –173 K.     

Quenched phosphorescence as alternative detection mode in the chiral separation of methotrexate by electrokinetic chromatography

Quenched phosphorescence was used, for the first time, as detection mode in the chiral separation of methotrexate (MTX) enantiomers by electrokinetic chromatography. The detection is based on dynamic quenching of the strong emission of the phosphorophore 1-bromo-4-naphthalene sulfonic acid (BrNS) by MTX under deoxygenated conditions. The use of a background electrolyte with 3 mg/mL 2-hydroxypropyl-β-cyclodextrin and 20% MeOH in 25 mM phosphate buffer (pH 7.0) and an applied voltage of 30 kV allowed the separation of l-MTX and its enantiomeric impurity d-MTX with sufficient resolution. In the presence of 1 mM BrNS, a detection limit of 3.2 × 10⁻⁷ M was achieved, about an order of magnitude better than published techniques based on UV absorption. The potential of the method was demonstrated with a degradation study and an enantiomeric purity assessment of l-MTX. Furthermore, l-MTX was determined in a cell culture extract as a proof-of-principle experiment to show the applicability of the method to biological samples.     

Optimization of a peroxyoxalate chemiluminescence detection system for the liquid chromatographic determination of fluorescent compounds

Summary A peroxyoxalate chemiluminescence detection system for liquid chromatography is described. The excitation of fluorophores is generated by the reaction of bis-(2,4,6-trichlorophenyl)oxalate or bis(2,4-dinitrophenyl)oxalate and hydrogen peroxide, which are added to the column effluent. The influence of the solvents and the concentrations of the reagents have been investigated. The influence of the flow cell volume on sensitivity and on band broadening have also been studied and a chemical band narrowing effect has been observed. Different types of apparatus have been compared for detection of the emitted light. The system has been used for the detection of the dansyl derivative of a drug with a secondary amine functional group in serum samples. The detection limits are in the 1–10pg range.     

Nonlinear Filtering in Rieznnnnifln Manifolds

A general formulation of the nonlinear filtering problem inRiemanman manifolds is given by use of the strong solutionsof the stochastic differential equations for the state and observationprocesses in the orthonormal frame bundles of the state andobservation process manifolds, respectively. A general Bayesformula for the conditional expectation of smooth functionsof the state process is given. This is used to give a directderivation of the Zakai equation for the general problem underconsideration. An example is presented.